Nonlinear optimal path control of a three axis robot manipulator

In this work the optimal path control of the tool point of a three axis robot manipulator has considered. The control problem has been found as a nonlinear and singular one. A simplified nonlinear model for a three axis robot arm has been obtained. The constrained and unconstrained optimal control problems have been solved to minimize the quadratic cost of error trajectories, the solution of the unconstrained optimal control problem has been found as the combination of regular and impulsive optimal inputs, as well as the optimal solution of the constrained optimal control problem has been found as the nonlinear on-off control.